NN Potential Research Articles

Chiral potentials, perturbation theory and the 1S0 channel of NN scattering

We use nucleon–nucleon phase shifts obtained from experimental data, together with the chiral expansion for the long-distance part of the NN interaction, to obtain information about the short-distance piece of the NN potential that is at work in the 1S0 channel. We find that if the scale R that defines the separation between ‘long-’ and ‘short-’ distance is chosen to be ≲1.8 fm then the energy dependence produced by short-distance dynamics is well approximated by a two-term polynomial for Tlab ⩽ 200 MeV. We also find that a quantitative description of NN dynamics is possible, at least in this channel, if one treats the long-distance parts of the chiral NN potential in perturbation theory. However, in order to achieve this we have to choose a separation scale R that is larger than 1.0 fm.

Roth and Navrátil Reply:

In their comment on our recent Letter [1] Dean et al. [2] criticize the calculations for the ground-state energy of {sup 40}Ca within the importance truncated no-core shell model (NCSM). In particular they address the role of configurations beyond the 3p3h level, which have not been included in the {sup 40}Ca calculations for large N{sub max} {h_bar}{Omega} model spaces. Before responding to this point, the following general statements are in order. For the atomic nucleus as a self-bound system, translational invariance is an important symmetry. The only possibility to preserve translational invariance when working with a Slater determinant basis is to use the harmonic oscillator (HO) basis in conjunction with a basis truncation according to the total HO excitation energy, i.e. N{sub max} {h_bar}{Omega}, as done in the ab initio NCSM. This is important not only for obtaining proper binding or excitation energies, but also for a correct extraction of physical wavefunctions. The spurious center-of-mass components can be exactly removed only if the HO basis and the N{sub max} {h_bar}{Omega} truncation are employed. The minimal violation of the translational invariance was one of the main motivations for developing the importance-truncation scheme introduced in the Letter. In this scheme, we startmore » with the complete N{sub max} {h_bar}{Omega} HO basis space and select important configurations via perturbation theory. All symmetries are under control and our importance-truncated NCSM calculations are completely variational and provide an upper bound of the ground-state energy of the system. The restriction to the 3p3h level, made for computational reasons in the N{sub max} > 8 calculations for {sup 40}Ca, is not inherent to the importance truncation scheme. The explicit inclusion of 4p4h configurations--though computationally more demanding--is straight-forward, even for the largest N{sub max} {h_bar}{Omega} model spaces discussed. To demonstrate this fact we have performed full 4p4h calculations for {sup 40}Ca in a 14{h_bar}{Omega} no-core model space at {h_bar}{Omega} = 24 MeV using the V{sub low k} interaction employed in the Letter. The resulting ground state energy of E{sub 4p4h} = -471.0 MeV can be compared with E{sub 3p3h} = -461.2 MeV for the 3p3h calculation reported in Fig. 5(b) with an uncertainty of typically 1 MeV due to the extrapolation {kappa}{sub min} {yields} 0. Thus the 4p4h configurations change the resulting ground-state energy of {sup 40}Ca by approximately 2%. In addition to the explicit inclusion of 4p4h or higher-order configurations in the importance truncated space, there are various other means to account for their effect on the energy. We are presently developing a perturbative method for the inclusion of up to 6p6h configurations using the ground state obtained from the NCSM diagonalization as unperturbed state. Furthermore, there are even simpler methods, such as multireference Davidson corrections, which are employed successfully in quantum chemistry [3], for estimating the contribution of excluded configurations to the energy. They even restore size extensivity in an approximate way. The coupled-cluster method (CCM) used by the authors of the Comment lacks the above discussed features important for the nuclear many-body problem, in particular it violates translational invariance from the very beginning and it does not fulfill the variational principle. The problem of a spurious center-of-mass contamination of the many-body states in CCM is not resolved and often not even mentioned (see e.g. Ref. [4]). Moreover, non-iterative triples corrections like CCSD(T), as referred to in the comment, tend to overestimate the correlation energy or even collapse. It is claimed that the CCM is very accurate. A closer inspection of recently published nuclear many-body results does not support this statement. In Ref. [5], the {sup 4}He binding energy with the chiral N{sup 3}LO NN potential was determined with an uncertainty of several MeV. The same is obtained in the ab initio NCSM with accuracy of 10 keV [6, 7]. The CCM binding energy results for {sup 16}O with the identical chiral N{sup 3}LO NN potential obtained in Refs. [8] and [9] differ by more than 5 MeV. According to Ref. [9], the CD-Bonn NN potential overbinds {sup 16}O. This is contrary to results obtained in Ref. [10] and also contrary to expectations as the CD-Bonn underbinds lighter nuclei. The CCSD(T) ground state energy for {sup 40}Ca with V{sub low k} reported in Ref. [4] is about 30 MeV lower than our 4p4h-result (CCSD is about 20MeV lower). Taking into account the small 2% difference of our 3p3h and 4p4h results and the violation of the variational principle and the translational invariance in the CCM method, we believe that the CCM result overestimates the exact ground-state energy in this case.« less

Polarization Effects in Elastic Electron-Deuteron Scattering and Their Dependence on Modern NN Potentials

Polarization Effects in Elastic Electron-Deuteron Scattering and Their Dependence on Modern NN Potentials

Formula omitted] system with chiral SU(3) effective interaction

The K−pp system is investigated using a variational approach with realistic two-body interactions: the Argonne v18 NN potential and an energy dependent K¯N effective interaction derived from chiral SU(3) coupled-channel dynamics. Uncertainties in subthreshold extrapolations of the K¯N interaction are considered. A weakly bound K−pp state is found, with a binding energy B=(19±3) MeV substantially smaller than suggested in previous calculations. The decay width Γ(K−pp→πΣN) is estimated to range between about 40 and 70 MeV.

RECENT RESULTS FOR THE BRAZILIAN TWO-PION EXCHANGE NUCLEON-NUCLEON POTENTIAL

We have recently performed a relativistic O(q4) chiral expansion of the two-pion exchange NN potential, and explored its configuration space content by fitting the theoretical expressions to parametrized simply formulas. In order to test the applicability of our parametrized potential, we studied the pion plus production in proton-neutron scattering at threshold an compare our results to the ones given by Reid 93 and v18 potentials. We shown that our results are very close to the v18 potential, which means that the potential is reliable and trustful.

Reaction cross sections for proton scattering from stable and unstable nuclei based on a microscopic approach

Reaction cross sections for proton-nucleus elastic scattering are investigated within a nonrelativistic microscopic approach for the nucleon-nucleus optical model potential. Applications were made for nucleon energy ranging between 10 MeV and 1 GeV, considering both stable and unstable target nuclei. The study is based on an in-medium g-matrix folding optical model approach in momentum space, with the appropriate relativistic kinematic corrections needed for the higher energy applications. The effective interactions are based on realistic NN potentials supplemented with a separable non-Hermitian term to allow optimum agreement with current NN phase-shift analyses, particularly the inelasticities above pion production threshold. The target ground-state densities are obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density-dependent Gogny force. The evaluated reaction cross sections for proton scattering are compared with measurements and their systematics is analyzed. A simple function of the total cross sections in terms of the atomic mass number is observed at high energies. At low energies, however, discrepancies with the available data are observed, being more pronounced in the lighter systems.

Nonlocal nucleon-nucleon interaction JISP

The J-matrix inverse scattering formalism is described and a new type of nucleon-nucleon interaction JISP is constructed within its framework. Interaction for each partial NN scattering is represented by a small matrix in the oscillator basis, which allows its direct use in multiparticle shell-model calculations and in calculations within the resonating group approximation. The JISP reproduces np scattering data and deuteron characteristics with an accuracy of modern realistic NN potentials (x2/datum = 1.05). The generalization of this interaction which takes into account violation of charge independence of nucleon-nucleon forces is proposed and pp scattering phases calculated with this new charge-dependent interaction CD-JISP are discussed.

Two-pion exchange NN potential from Lorentz-invariant χEFT

We outline the progress made in the past five years by the Sao Paulo group in the development of a two-pion exchange nucleon-nucleon potential within a Lorentz-invariant framework of (baryon) chiral perturbation theory.

Experimental study of neutron-neutron quasifree scattering in thendbreakup reaction at 25 MeV

Neutron-neutron quasifree scattering in the nd breakup reaction at 25 MeV has been investigated. The absolute cross section was determined with an accuracy of a few percentages, normalized by np scattering, which was measured simultaneously. The data were analyzed by detailed Monte Carlo simulations based on rigorous 3N Faddeev-type calculations using the CD-Bonn NN potential. The measured cross-section data in this experiment are (16.0 {+-} 4.6)% larger than the theoretical predictions.

Baryonic 3P2-Dominant Superfluidity under Combined Pion Condensation with Isobar. II: Properties of Pairing Interaction and Numerical Results

According to the formulation developed in I, we calculate energy gaps of the baryonic 3 P2dominant superfluidity under the combined pion condensation with ∆-mixing at moderately high density in neutron star interior. Adopting a baryon-baryon potential extended from a“ root” NN potential to be workable in theN + ∆ space, we obtain the concrete form of the pairing interaction matrix elements between the quasi-baryon pairs, which constitute a two-dimensional angular-momentum stretched state and a charge triplet. With use of OPEG-B as a “root” NN potential and an available set of the parameters representing the combined pion condensation, we study the properties of two-dimensional pairing potentials and the matrix elements of pairing interaction. We find that the strong attraction of pairing interaction for the quasi-neutron pairs is brought about by the spin-orbit potential and the spin- and isospin-dependent core terms of the central potential, whose effects are enhanced due to the pion condensation. The quasi-neutron pair plays a decisive role to bring about meaningful energy gaps, while the coupling between different quasi-baryon pairs plays no important role, as a consequence of a unique feature of the combined pion condensation we adopt. We numerically solve the energy gap equation for baryon density of (2 − 6) times the nuclear density and clarify substantial aspects of resulting superfluid energy gaps, and discuss related problems by taking into account possible change in the factors affecting the energy gaps, such as baryon-baryon potentials, some of the pion condensation parameters and an effective mass of the quasi-particle. Standing on these results, we can say that the 3 P2-dominant superfluid is realized with the critical temperatures Tc of the order of 10 9 K, equivalent to the energy gaps of the order of 0.1 MeV, under the combined pion condensation in neutron star matter. The key point of the recognition lies in the aspects that the ∆-mixing provides the additional pairing attraction of short range, although the attenuation of the pairing attraction due to the charged-pion condensation comes about in the whole interaction range. This means that the superfluid of this type can provide the meaningful suppression on the emissivity of the pion direct Urca process, which makes the pion cooling scenario of neutron stars available.

Leading-order 2πγ exchange NN interaction: Central potentials proportional to gA 0 and gA 2

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the leading-order 2π exchange NN interaction proportional to gA0 and gA2. The resulting 2πγ exchange potential contains isospin-breaking components which reach up to about -2% of the corresponding isovector 2π exchange potential. With a value of only -17keV at r = mπ-1 = 1.4fm the charge-independence breaking central potential obtained here is negligibly small in comparison to the one generated by the isoscalar c3 contact vertex. Our calculation confirms that the largest long-range isospin-violating NN potentials arise from the 2πγ exchange diagrams involving the large low-energy constants c4 ≃ - c3 ≃ 3.3GeV^-1 representing the important Δ(1232) dynamics.

Nuclear Structure in the UCOM Framework: From Realistic Interactions to Collective Excitations

The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the no-core shell model provides insight into the interplay between dominant short-range and residual long-range correlations in the nuclear many-body problem. The use of the correlated interaction within Hartree-Fock, many-body perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.

ΛΛ 6 He and ΛΛ interaction

A phenomenological potential of ΛΛ interaction is found on the basis of a treatment of ΛΛ6He as a six-particle system. The semirealistic ΛN and NN potentials used in this treatment ensure an adequate description of the binding energies of 1s-shell hypernuclei and Λp scattering, as well as of the binding energies and dimensions of the nuclear cores. The reliability and a high precision of the calculations are achieved owing to determining both an upper and a lower bound on the energies in question. A cluster model involving the Λα potential matched with the results of precise calculations for the 4He, Λ5He, and ΛΛ6He systems is used to calculate ΛΛ10Be and other double heavy hypernuclei and to analyze the possibility of a consistent description of all double hypernuclei.

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors⋆

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ¯(k f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ0 ≃ 0.16fm^-3, ¯0 ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ¯(k f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈¯q〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ0 we find small corrections from the derivative d¯(k f)/dm π, which are stable against variations of the monopole regulator mass Λ.

QUENCHING OF THE DEUTERON IN FLIGHT

We investigate the Lorentz contraction of a deuteron in flight. Starting from the Blankenbecler-Sugar projection of the Bethe-Salpeter equation to a 3-dimensional quasi potential equation, we apply it for the deuteron bound in an harmonic oscillator potential (for an analytical result) or by the Bonn NN potential for a more realistic estimate. We find substantial quenching with increasing external momenta and a significant modification of the high momentum spectrum of the deuteron.

Analyzing powers and spin correlation coefficients forp+delastic scattering at 135 and 200 MeV

The proton and deuteron analyzing powers and ten of the possible 12 spin correlation coefficients have been measured for p+d elastic scattering at proton bombarding energies of 135 and 200 MeV. The results are compared with Faddeev calculations using two different NN potentials. The qualitative features of the extensive data set on the spin dependence in p+d elastic scattering over a wide range of angles presented here are remarkably well explained by two-nucleon force predictions without inclusion of a three-nucleon force. The remaining discrepancies are, in general, not alleviated when theoretical three-nucleon forces are included in the calculations.

Shell-model description of 16C with the Idaho N3LO NN potential

The structure of the neutron-rich carbon nucleus 16C is described within a new microscopic shell-model framework. The model space is composed of the 0s, 0p, 1s0d and 1p0f shells, and thus a sort of no-core type. The effective interaction is microscopically derived from the Idaho N3LO NN potential and the Coulomb force through a unitary transformation theory. Calculated low-lying energy levels of 16C agree well with the experimental values. Furthermore, the anomalously hindered B(E2; 2+1 → 0+1) value for 16C, measured recently, is well described by the calculation with the bare charges.

Erratum: Neutrino reactions on the deuteron [Phys. Rev. C 63, 034617 (2001)

The cross sections for the \nu-d and \bar{\nu}-d reactions are calculated for the incident energy up to E_\nu = 170 MeV, with the use of a phenomenological Lagrangian approach. We assess and improve the reliability of the employed calculational method by examining the dependence of the results on various input and approximations that go into the calculation. The main points of improvements over the existing work are: (1) use of the "modern" NN potentials; (2) use of the more accurate nucleon weak-interaction form factors; (3) monitoring the strength of a vertex that governs the exchange-current contribution, with the use of data on the related process, n+p\to d+\gamma. In addition to the total cross sections, we present various differential cross sections that are expected to be useful for the SNO and other experiments. In the low energy regime relevant to the solar neutrinos, the newly calculated total cross sections agree with the existing literature values. The origins of slight differences found for higher energies are discussed. The ratio between the neutral-current and charged-current reaction cross sections is found to be extremely stable against any variations in the input of our calculation.

Testing nuclear forces by polarization transfer coefficients ind(p→,p→)dandd(p→,d→)preactions atEplab=22.7MeV

The proton to proton polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'} and the proton to deuteron polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'}, K_x^{y'z'}, K_y^{z'z'}, K_z^{y'z'}, K_y^{x'z'} and K_y^{x'x'-y'y'} have been measured in d(\vec p, \vec p)d and d(\vec p, \vec d)p reactions at E^{lab}_p = 22.7 MeV, respectively. The data have been compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi) phenomenological nucleon-nucleon potentials combined with model three-nucleon forces and modern chiral nuclear forces have been used. The AV18, CD Bonn, Nijm I and II nucleon-nucleon interactions have been applied alone or combined with the Tucson-Melbourne 99 three-nucleon force, adjusted separately for each potential to reproduce the triton binding energy. For the AV18 potential also the Urbana IX three-nucleon force have been used. In addition chiral NN potentials in the next-to-leading-order and chiral two- and three-nucleon forces in the next-to-next-to-leading-order have been applied. Only when three-nucleon forces are included a satisfactory description of all data results. For the chiral approach the restriction to the forces in the next-to-leading order is insufficient. Only when going over to the next-to-next-to-leading order one gets a satisfactory description of the data, similar to the one obtained with the (semi) phenomenological forces.

Pion-photon exchange nucleon-nucleon potentials

In chiral perturbation theory, the dominant next-to-leading-order correction to the {pi}{gamma}-exchange NN-potential proportional to the large isovector magnetic moment {kappa}{sub v}=4.7 of the nucleon is calculated. The corresponding spin-spin and tensor potentials V{sup {approx}}{sub S,T}(r) in coordinate space have a very simple analytical form. At long distances, r{approx_equal}2 fm, these potentials are of similar size (but opposite in sign) as the leading-order {pi}{gamma}-exchange potentials. Effects from virtual {delta}-isobar excitation are also considered, as well as other isospin-breaking contributions to the 2{pi}-exchange NN potential induced by additional one-photon exchange.